Camera Calibration for Synthetic Digital Tomography Michael Albert, Ann-Katherine Carton, Andrew D.A. Maidment Department of Radiology, University of Pennsylvania, Philadelphia, PA 19104 ABSTRACT A method for calibrating camera geometry is described. This method has been used to implement synthetic tomography on a commercially available full-field digital mammography system. The method utilizes a phan- tom containing six point-like calibration objects whose positions are approximately known. The image of five calibration objects in a given projection allows an associated projection matrix to be determined up to one free parameter. By using the positions of the shadows of the sixth calibration object in three or more views, one can fit the remaining free parameter associated with each view and the position of the sixth calibration object relative to the first five. Uncertainty in the position or geometry of the phantom does not affect the geometric consistency, thus tomograms produced by back–projection suffer no blurring from errors in the determination of camera geometry. Uncertainties in the position or geometry of the phantom result in proportionate translations or distortions of the tomograms. For a tomogram corresponding to a plane containing an object, the positions of the backprojections of the shadows of the object are consistent to the same precision as the measurements of the shadows in each projection, i.e., the positions of the backprojections differ by about the size of the pixel spacing in the detector. Keywords: Synthetic tomography, camera calibration, projective geometry, digital mammography 1. INTRODUCTION A significant limitation on the efficacy of projection imaging is imposed by the inherent summation of multiple layers of anatomy. This “anatomical noise” can produce both false-negatives, as when a lesion is obscured by overlying anatomy, and false–positives or “summation artifacts,” as when a lesion is not properly distinguished from the clutter produced by the summation of various layers of normal anatomy. The importance of anatomical noise has been studied in the context of a variety of medical–imaging tasks including chest radiography 1 and mammography. 2 Synthetic tomography combines multiple projections acquired at distinct angles to produces images focused on a given anatomical plane, while other anatomical planes are blurred. The utility of tomography in overcoming anatomical noise is discussed in the review by Samei, Eyler and Baron. 3 In order to combine information from the various projections it is important to have accurate geometric information. To be explicit, let (x, y, z ) represent the coordinates of a point in space, and let (u α ,v α ) represent the position on an area detector where the x–ray shadow of that point falls. The index α indicates which image, of a series of acquired images, is being considered. Accurate geometric knowledge allows one to determine functions f α such that (u α ,v α )= f α (x, y, z ). (1) The observation of the shadow of a point–like object in a projection gives two constraints on three unknowns, thus, as x–rays travel in straight lines, determining a line upon which the object must lie. Because of uncertainties in geometrical information, the lines determined from the various views will generally be skew and there will Further author information: (Send correspondence to A.D.A.M.) M.A. E-mail: michael.albert@uphs.upenn.edu A.–K.C. E-mail: ann-katherine.carton@uphs.upenn.edu A.D.A.M.: E-mail: andrew.maidment@uphs.upenn.edu, Telephone: 215–746–8763, Address: Dept. of Radiology, 1 Silverstein, 3400 Spruce St., Philadelphia, PA 19104 Medical Imaging 2005: Physics of Medical Imaging, edited by Michael J. Flynn, Proceedings of SPIE Vol. 5745 (SPIE, Bellingham, WA, 2005) 1605-7422/05/$15 · doi: 10.1117/12.597316 1291 DownloadedFrom:http://spiedigitallibrary.org/on07/15/2016TermsofUse:http://spiedigitallibrary.org/ss/TermsOfUse.aspx